I've got to ask, unless your music collection is just huge, why not "sneaker net" to work on a thumb drive?
On to the challenge...
You said Squeezecenter uses port 9000 for music? Does it use another port for control? I don't remember. That's smart to alias the port to confuse any hackers. Still, I would look into also only allowing the IP of your work place access to your home network (if at all possible (i.e. you firewall needs this feature and your work's IP needs to be static)). Using the IP number is easier then using a domain name. If you use a domain name your program (the squeezecenter client on the chumby) would have to then know about a DNS to convert the name to an IP number. But I have to ask, can the chumby squeezecenter client use a different port number? It should be easy - but last I implemented a squeeze center client, I don't think I gave the end user that option.
So, does anyone know if the source code for the squeezecenter client is available. You could have a look at that and try your hand at involving a DNS as part of the package. That way you could enter your domain name and have the chumby look up the IP number from an outside DNS.
If that turns out to be difficult (although there should be plenty of canned examples of DNS look ups), maybe there's a way the chumby squeezecenter client can ask your dynamicDNS service for the IP number. Like scrape a web page given a URL which includes your domain name as an argument for instance.
What would I do? My provider doesn't change my IP very often. I would probably be lazy about it, look it up and use that number until it stopped working. Then look up the new number again.
Be warned, some companies don't like streaming and have locked such protocols out with one type of method or other.
-good luck